0,2

Joe Keane (jgk(AT)jgk.org) observes that this sequence (beginning at 3) is "size of raises in pot-limit poker, one blind, maximum raising".

It appears that this sequence is the BinomialMean transform of A001653 (see A075271). - John W. Layman (layman(AT)math.vt.edu), Oct 03 2002

Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 8 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = 3, s(2n+1) = 4. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 12 2004

Hwang, F. K.; Mallows, C. L.; Enumerating nested and consecutive partitions. J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333.

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 164

N. J. A. Sloane, Transforms

Index entries for sequences related to poker

a(n+1)=4a(n)-2a(n-1). G.f.: (1-x)/(1-4x+2x^2). Binomial transform of Pell numbers 1, 2, 5, 12, ... (A000129).

G.f.: (1-x)/(1-4x+2x^2).

a(n)=(A035344(n)+1)/2; a(n)=(2+sqrt(2))^n(1/2+sqrt(2)/4)+(2-sqrt(2))^n(1/2-sqrt(2)/4). - Paul Barry (pbarry(AT)wit.ie), Jul 16 2003

Second binomial transform of (1, 1, 2, 2, 4, 4, ...). a(n)=sum{k=1..floor(n/2), C(n, 2k)2^(n-k-1)}. - Paul Barry (pbarry(AT)wit.ie), Nov 22 2003

a(n)=( (2-Sqrt(2))^(n+1)+(2+Sqrt(2))^(n+1) )/4. - Herbert Kociemba (Kociemba(AT)t-online.de), Jun 12 2004

a(n) = both left and right terms in M^n * [1 1 1], where M = the 3X3 matrix [1 1 1 / 1 2 1 / 1 1 1]. M^n * [1 1 1] = [a(n) A007070(n) a(n)]. E.g. a(3) = 34. M^3 * [1 1 1] = [34 48 34]. (center term is A007070(3)) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 18 2004

The i-th term of the sequence is the entry (2, 2) in the i-th power of the 2 by 2 matrix M=((1, 1), (1, 3)). - Simone Severini (ss54(AT)york.ac.uk), Oct 15 2005

E.g.f. : exp(2x)(cosh(sqrt(2x)+sinh(sqrt(2)x)/sqrt(2) - Paul Barry (pbarry(AT)wit.ie), Nov 20 2003

(PARI) a(n)=real((2+quadgen(8))^(n+1))/2

a(n)=A006012(n+1)/2=A056236(n+1)/4. Cf. A003480.

Cf. A007070.

Sequence in context: A034215 A083580 A113300 this_sequence A048580 A059738 A094832

Adjacent sequences: A007049 A007050 A007051 this_sequence A007053 A007054 A007055

nonn,easy

Colin Mallows, njas, Simon Plouffe (plouffe(AT)math.uqam.ca)